Limits of control for quantum systems: Kinematical bounds on the optimization of observables and the question of dynamical realizability - art. no. 025403

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for nondissipative quantum sys tems imposes kinematical bounds on the optimization of arbitrary observable s. We summarize our previous results on kinematical bounds and show that th ese bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable s ystems. Finally, the question of dynamical realizability of the bounds for arbitrary partially controllable systems is shown to depend on the accessib le sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.